The continuous-time equations need to be discretized before
implementation. When discretizing the traditional inertial
navigation equations in (REF ) it is commonly
assumed that the angular velocity and the specific
force are constant between each sample instant [1]}.
However, since the inertial sensor array also provides an
estimate of the angular acceleration, the discretization of the
rotation matrix in
(REF ) can instead
be based on the assumption of constant angular acceleration. For the
angular velocity, position, and velocity, which are expressed in
Euclidean vector-spaces, the discretization can be found by truncating
the Taylor series given by
\(\omega (t + T)&= \omega (t) + \dot{\omega }(t)T + \mathcal {O}(T^2),\\p(t+T)&= p(t) + v(t)T + \dot{v}(t)\frac{T^2}{2} + \mathcal {O}(T^3),\\v(t+T)&= v(t) + \dot{v}(t)T + \mathcal {O}(T^2).\) 
